Well currently many people keep their printer in their home, so it could be problematic having people come and go from your house to 3D print things. One alternative is for the person who houses the printer to do all of the physical labor associated with printing, i.e. starting prints, leveling the bed, maintenance, etc. But this is NOT a negligible amount of time, and so this person would be doing more than a free amount of work. Maybe you could pay that person for the effort, but most people would be time-sharing a printer to save money in the first place. Another alternative is to keep the printer in a mutally accessible space, but if this is a public space, you have to worry about theft of services (strangers using the printer) or theft of the printer itself. So yes, to put it simply, logistics can be an issue.
If you found a way to overcome all of that, then "a tool to manage it" is just a basic scheduler. People would block off time on the schedule for their prints, using software estimates of print time (with a healthy buffer for things to go wrong) and ensure that they could be there both at the start and end of their print time for set up and clean up. So I guess what you're proposing is a fancy Excel sheet?